Question

select the correct answer.
which expression is equivalent to the given polynomial expression?
$(-4a^2 - 3b) + (-2ab - a^2 + b^2) + (-b^2 + 6ab)$
a. $-3a^2 + 2b^2 + 8ab + 3b$
b. $-3a^2 + 4ab + 3b$
c. $-5a^2 + 2b^2 + 8ab + 3b$
d. $-5a^2 + 4ab - 3b$

Explanation:

Step1: Remove parentheses

Remove the parentheses from the expression \((-4a^{2}-3b)+(-2ab - a^{2}+b^{2})+(-b^{2}+6ab)\) to get \(-4a^{2}-3b - 2ab - a^{2}+b^{2}-b^{2}+6ab\).

Step2: Combine like terms for \(a^{2}\) terms

Combine the \(a^{2}\) terms: \(-4a^{2}-a^{2}=-5a^{2}\).

Step3: Combine like terms for \(b^{2}\) terms

Combine the \(b^{2}\) terms: \(b^{2}-b^{2} = 0\).

Step4: Combine like terms for \(ab\) terms

Combine the \(ab\) terms: \(-2ab + 6ab=4ab\).

Step5: Combine like terms for \(b\) terms

Combine the \(b\) terms: \(-3b\) (there are no other \(b\) terms to combine with it in this case, but we keep it as is).
Putting it all together, the simplified expression is \(-5a^{2}+4ab - 3b\).

Answer:

D. \(-5a^{2}+4ab - 3b\)